# A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

@article{Williams2015ADA, title={A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition}, author={Matthew O. Williams and Ioannis G. Kevrekidis and Clarence W. Rowley}, journal={Journal of Nonlinear Science}, year={2015}, volume={25}, pages={1307-1346} }

The Koopman operator is a linear but infinite-dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system and is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. In this manuscript, we present a data-driven method for approximating the leading eigenvalues, eigenfunctions, and modes of the Koopman operator. The method requires a data set of snapshot pairs and a dictionary of scalar…

## 816 Citations

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A new algorithm for the finite dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time series data is provided, described as naturally structured DMD since it retains the inherent properties of these operators.

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